Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX-XXX
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Effects of the Cage Number and Excess Electron Number on the Second Order Nonlinear Optical Response in Molecular All-Metal Electride Multicage Chains Hui-Min He,† Ying Li,† Hui Yang,†,‡ Dan Yu,† Di Wu,*,† Rong-Lin Zhong,† Zhong-Jun Zhou,† and Zhi-Ru Li*,† †
Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023, China ‡ School of Chemistry and Chemical Engineering, Shanxi Datong University, Daton 037009, China S Supporting Information *
ABSTRACT: For novel all-metal electride, multicage chain structures [(Ni@ Ge9) Ca3]n (n = 1−4) with all real frequencies are obtained theoretically for the first time. In the structure of n = 1, the Ni@Ge9 metal cage as the shortest chain skeleton is surrounded by nonbridge Ca atoms. In the structures of n = 2−4, Ni@Ge9 metal cages are connected by bridge Ca atom pair(s) forming new hybrid multicage chain skeletons surrounded by nonbridge Ca atoms. And interesting pull−push electron relay occurs. The chain skeleton pulls valence electrons from nonbridge Ca atoms forming skeleton polyanion, and then formed polyanion pushes remaining valence electrons of the Ca atoms forming excess electrons. The excess electron numbers are Ne = 2, 0, 4, 4 for n = 1, 2, 3, 4, respectively. It is shown that these structures with excess electrons are molecular all-metal electride multicage chains, unexpectedly, and the structure (n = 2) without excess electron is a Ca salt. For nonlinear optical (NLO) response, the electride chains have large static first hyperpolarizabilities (βe0). And βe0 increases strongly from 9321 (n = 1, Ne = 2) to 54232 au (n = Ne = 4), which exhibits that significant cage number and excess electron number effects on NLO response. Besides electronic contribution (βe0) to static first hyperpolarizability, the large nr e vibrational contribution (βnr 0 ) are also revealed, and the ratios of β0 /β0 are 0.18−1.17. Moreover, the frequency-dependent values e e β (−2ω; ω, ω) and β (−ω; ω, 0) have also been estimated. Especially, the evolutions of prominent cage number effects on βe0, e e βnr 0 , β (−2ω; ω, ω) and β (−ω; ω, 0) are similar. Then a new design strategy of enhancing NLO response by increasing metalcage number is obtained. Hence, these molecular all-metal electride multicage chains as novel nanorods are promising new NLO nanomaterials. satisfactory βe0, they do not have high thermostability due to used organic complexant. Obviously, new kind of electride NLO molecules should be expected and researched. Experimental and theoretical studies have shown that allmetal extended Zintl polyanions20−24 are more capable of pushing the valence electrons of an electron donor to form excess electrons. Having an insight into polar intermetallic compounds with Zintl polyanions, we have proposed a new concept “all-metal electride” and designed and researched allmetal electride NLO molecules CuAg@Ca7M (M = Be, Mg and Ca).25 In these molecules, alkaline-earth-metal atom Ca serves as the electron source, and meanwhile extended Zintl polyanions [Cu−Ag−Be/Mg]4− and [Cu−Ag]4− act as complexants to push the valence electrons of Ca atoms. This research shows that [(Ca2+)7(CuAgMg)4−] + 10e− has large βe0
1. INTRODUCTION Molecular nonlinear optical (NLO) materials are numerous and attract considerable interest in account of the promise they hold for applications in emerging optoelectronic and all-optical data processing technologies.1−3 Intriguing electride NLO molecules4−11 with excess electron anions is a fast-growing activity field. This is because that introducing excess electrons into a molecule is an effective approach to prominently enhance its NLO response by enhancing its static first hyperpolarizability.12,13 Shortly afterward, a series of new strategies have been proposed to enhance the NLO response and electronic stability of the electride molecules by regulating molecular and electronic structure properties of complexants14 and manipulating the number and spin state of excess electrons.15 In the previous studies,16−19 an amount of electride molecules were designed by doping alkali metal atoms into different kinds of organic complexants. These electride molecules have large first hyperpolarizabilities (βe0). It can be noted that although electride molecules usually possess a © XXXX American Chemical Society
Received: July 4, 2017 Revised: October 20, 2017 Published: October 23, 2017 A
DOI: 10.1021/acs.jpcc.7b06464 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
Figure 1. Optimized structures of molecular all-metal multicage chain [(Ni@Ge9)Ca3]n (1, 2, 3, and 4) at the PBE0 level.
of 1.43 × 104 au. In additional, we also obtained theoretically all-metal NLO switches, i.e. all-metal electrides M(Ni@Pb12)M (M = Be, Mg, and Ca) as novel external electric field driven NLO switches.26 Both of aforementioned systems belong to zero-dimensional electride nanosystems. One-dimensional nanosystem is one of most exciting research areas and has brought us many surprises. Manufactured nanolaser is the most wizardly example.27,28 Onedimensional metal nanomaterials have been also manufactured including Cu−,29,30 Ag−,31,32 and Au−nanowire,33,34 and drawn widespread concern and research because of excellent optical, electrical, magnetic and other properties from dimension effect, and molecular and electronic structures. It is worth noting that one-dimensional molecular all-metal electride has been not reported. Naturally, a logical consideration occurs. Constructing one-dimensional molecular all-metal electrides and exploring their structures and properties are meaningful and expected. Fortunately, the chemistry of nine-atom Zintl anions gives us the opportunity to design novel molecular all-metal electride multicage chain, and then we can further explore evolution of the molecular all-metal electrides toward one-dimensional materials. As infinite chains of germanium clusters such as [Ge9−Ge9]6−,35 [Ge9Ge9 Ge9]6−,36 and [Ge9Ge9Ge9Ge9]8−37,38 have been synthesized, they may act as potential chain-shaped pushing electron complexants. We select better all-metal cage Ni@Ge939,40 stabilized by the interaction between the Ge9 cage and the encapsulated Ni atom, as potential complexant unit and alkaline-earth-metal Ca atoms as the electron source to construct all-metal electride multicage chain series [(Ni@Ge9) Ca3]n (1, 2, 3, and 4). In the chains, all-metal Zintl polyanions (Ni@Ge9)2− or (Ni@Ge9)4− are formed by gaining some valence electrons from Ca atoms and in turn push the remaining valence electrons of Ca atoms to form excess electrons. Our research has found that some Ca
atoms really serve as the electron source. But others are present in pair and each Ca-pair as a bridge inserts into between two adjacent Ni@Ge9 cages and cuts off preconceived Ge−Ge links, which increases systemic stability. In this paper, we will exhibit molecular and electronic properties and dimension effects on NLO response, especially, effects of the cage number and excess electron number on NLO response.
2. COMPUTUTIONAL METHODS The exact-exchange-incorporated PBE0,41−45 the most satisfactory functional for the molecular structures containing transition metals,46,47 is selected to calculate optimum geometric structure and vibrational frequency of these molecular all-metal electride multicage chains. For the structures and some properties of the larger complexes with trans-metal atom, the TPSSh/6-31G*/LANL2DZ level (on the transition metal)48 and the 6-31+G** + LANL2DZ (on the transition metal) mixed basis set coupled with B3LYP have used.49 Then the Los Alamos double-ζ type set LANL2DZ50−52 for Ni and Ge and Pople-type basis sets53 6-31g for Ca, are selected. The vertical ionization potential (VIP) and chain scission energy (Ecs) calculations are also performed at the PBE0 level in conjunction with LANL2DZ for Ni and Ge, and the 6-31g basis set for Ca. The vertical ionization potential (VIP) is noted as follows:18 VIP = E[M+] − E[M]
where the energies E[M+] and E[M] are calculated at the optimum geometry of the neutral molecule. We use countpoise procedure54,55 to accurately calculate chain scission energy Ecs (see Figure 1): B
DOI: 10.1021/acs.jpcc.7b06464 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C Ecs1 + [(Ni@Ge9)Ca3]n = [(Ni@Ge9)Ca3]m + (Ni@Ge9)Ca3,
βi =
(i, j = x, y, and z) for the electro-optical Pokcets effect (EOPE). All of the calculations were carried out using the Gaussian09 program package.68 Molecular orbitals were visualized with the GaussView program.69
for n = 2, 3, 4 and m = n − 1; Ecs2 + [(Ni@Ge9)Ca3]4 = [(Ni@Ge9)Ca3]2 + [(Ni@Ge9)Ca3]2
3. RESULTS AND DISCUSSION 3.1. Equilibrium Geometries. We doped three alkalineearth metal Ca atoms on all-metal cage Ni@Ge9 designing a molecular all-metal electride monomer, where the former acts as electron source and the latter behaves as potential electronpushing complexant. The unusual all-metal cage Ni@Ge9 is further stabilized by the interaction between the Ge9 cage and the encapsulated Ni atom.39 In the molecular all-metal electride monomer, the Ni@Ge9 cage becomes an electron-pushing complexant of all-metal Zintl polyanion when it seizes valence electrons from Ca atoms. Linking such monomers may form molecular all-metal electride polymer chains. The optimized structures of [(Ni@Ge9) Ca3]n (1, 2, 3, and 4) with all real frequencies are shown in Figure 1. In the optimized structure of monomer (Ni@Ge9)Ca3, we can see that the Ni@Ge9 has approximate C4v-symmetric monocapped square antiprism geometry and the Ni atom is located in the center of the square antiprism. And the monocapped square antiprism Ni@ Ge9 is further capped by 3 Ca atoms. For polymers (n = 2−4), optimized results are interesting. An initial structure of (Ni@Ge9)n cage chain skeleton surrounded by Ca atoms converts into novel molecular allmetal multicage chain structure. Thus, besides some Ca atoms doped on the cage(s), the rest of the Ca atoms are present in pair(s), each Ca-pair as a bridge inserts into between two adjacent Ni@Ge9 cages and cut off preconceived Ge−Ge links forming the lower energy structure. Then, all Ca atoms are classified into two categories: bridge atoms and nonbridge atoms. The Ca-pair as a bridge connects two adjacent Ni@Ge9 metal cages forming the new hybrid chain skeleton. The remaining Ca atoms as nonbridge atoms surrounding Ni@Ge9 cages are monocapped (one Ca as a cap) and bicapped atoms (a Ca-pair as a cap) on 4Ge-rings. The total Ca atom number is 3n for n = 1−4. Consider the Ca atom numbers of the two types, bridge atom numbers are 0, 2, 4, and 6 following 2(n − 1) rule, and the nonbridge atom numbers are 3, 4, 5, and 6 for n = 1, 2, 3, and 4. Further consider different types of nonbridge atoms as follows: monocapped atom numbers are 1 for n = 1 and 0, 1, and 2 exhibiting an n − 2 rule for n = 2−4; bicapped atom numbers are 2 in one side for n = 1, and 4 in two sides for n = 2−4. According to the Ca atoms classification, [(Ni@ Ge 9 )Ca 3 ] 4 may be written as Ca 2 [Ca 6 (Ni@Ge 9 ) 4 ]Ca 4, representing two monocapped Ca atoms and six Ca atoms as bridges linking four Ni@Ge9 cages and four bicapped Ca atoms, respectively. Some interatomic distances are also exhibited in Figure 1. In the monomer Ni@Ge9Ca3 molecule, Ge−Ge distance is in the range of 2.628−3.376 Å that is considerably longer than Ge− Ge single bond range of 2.5−2.9 Å in empty Ge9 cage.70 This is because the Ge9 cage is dilated by the encapsulated Ni atom and influenced by doped Ca atoms. As a whole consideration, molecular chain lengths of the all-metal multicage chain molecules should be exhibited. As one dimension nanochain length is represented by the largest Ca···Ca distance (L), the Lvalues are nanoscale: 7.94, 16.32, 21.91, and 31.86 Å for n = 1,
It is known that the second-order Møller−Plesset perturbation (MP2) method is more acceptable than DFT in static first hyperpolarizability calculations,16,56 but it is very costly for the larger systems. Kirtman and his co-workers have find B3LYP is a suitable DFT method for calculating hyperpolarizabilities of molecular electrides.57 In this work, we have selected the MP2 and some DFT methods for a contrastive study to find a suitable DFT method. According to the test results (Table 1), Table 1. First Hyperpolarizabilities (βe0) Calculated by Different Density Functionals with LANL2DZ/6-31g monomer dimer trimer tetramer
MP2
B3LYP
PBE0
B3PW91
13923 23
9321 27 21937 54232
8876 31 16072 23987
9040 23 18635 38563
for monomer and dimer, the results of the B3LYP are close to those of the MP2. Therefore, the B3LYP is suitable and has selected for calculating hyperpolarizabilities of these all-metal electride chains. The basis set effects in accurately calculating the first hyperpolarizabilities have studied for some smaller and larger molecules.58−62 Here we use the LANL2DZ for Ni and Ge and the 6-31g basis set without diffuse functions for Ca, in order to avoid nonmatching basis sets of different atoms. Table S1 shows the basis set effect results, and focused evolutions of prominent cage number effect on βe0 are similar. The static first hyperpolarizability (βe0) is noted as follows: β0e = (βx 2 + βy 2 + βz 2)1/2
where βi =
3 (β + βijj + βikk ); i , j , k = x , y , z 5 iii
Similarly, according to the Bishop and Kirtman theory63,64 with double-harmonic approximation, we also estimate the static vibrational first hyperpolarizabilities using B3LYP method in conjunction with the LANL2DZ for Ni and Ge and the 631g basis set for Ca for these all-metal molecule chains. The frequency-dependent first hyperpolarizabilities of these molecular all-metal electrides were obtained by the coupled perturbed Hartree−Fock (CPHF) method.65,66 The basis set employed are the LANL2DZ for Ni and Ge and the 6-31g basis set for Ca. The frequency-dependent is noted as67 β e(ω) = (βx 2 + βy 2 + βz 2)1/2
Where βi =
1 [β ( −ω; ω , 0) + 2βjij( −ω; ω , 0)] 5 jji
1 [2β ( −2ω; ω , ω) + βijj( −2ω; ω , ω)] 5 jji
(i, j = x, y, and z) for the second-harmonic generation (SHG) and C
DOI: 10.1021/acs.jpcc.7b06464 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 2. Frontier occupied orbitals of in the all-metal molecular chains. 2e− represents two excess electrons.
molecular all-metal electride chain and can be represented as (Ca2+)2 [Ca6(Ni@Ge9)4]8−(Ca2+)4 (4e−). Summary, with increasing chain length (cage number n), the evolutions of the excess electron numbers and polyanion chain valences (V) are complex: Ne = 2, 0, 4, 4; V = −4, −8, −6, −8 for n = 1, 2, 3, and 4. This shows that these structures with excess electrons are molecular all-metal electride multicage chains, but the dimer chain (n = 2) without excess electron is an all-metal Ca salt multicage chain. 3.3. Electronic and Molecular Stabilities. For molecular electrides, the electronic stability is important due to the existence of loosely bound excess electrons. The electronic stability of a molecule may be characterized by its first vertical ionization potential (VIP) value. From Table 2 and Figure 3,
2, 3, and 4 (see Figure 1). Then the all-metal multicage chain molecules can be new nanorods. 3.2. Electride Characteristic of [(Ni@Ge9)Ca3]n (n = 1− 4) Chains. In these molecular all-metal multicage chains, a pull−push electron transfer relay occurs. The chain skeletons pull valence electrons from nonbridge Ca atoms forming allmetal polyanion chains, further the polyanion chains push the remaining valence electrons of the nonbridge Ca atoms forming excess electrons. Next, the excess electron numbers and valences of all-metal polyanion chains will be discussed. Molecular excess electron number is total occupation number of excess electron orbitals. And excess electron orbitals are the molecular orbitals with high energy level and pushed slobe from Ca atom(s). Figure 2 shows the frontier occupied orbitals of the all-metal molecular chains. The orbitals with 2e− are doubly occupied excess electron orbitals. For the monomer Ca(Ni@Ge9)Ca2, the highest occupied molecular orbital (HOMO) is a doubly occupied excess electron orbital. Therefore, the monomer Ca(Ni@Ge9)Ca2 with two excess electrons has electride characteristic. Considering the roles of valence electrons from Ca atoms, the three nonbridge Ca atoms provide six valence electrons. Here, two valence electrons are responsible for the excess electrons of Ne = 2. And the remaining four valence electrons are taken away by Ni@Ge9 forming the Zintl polyanion (Ni@Ge9)4− looking like the empty (Ge9)4− structure of C4v-symmetric monocapped square antiprism,71 as electron-pushing complexant. Obviously, the molecular all-metal electride monomer can be described as saltlike (ionic compound) Ca2+(Ni@Ge9)4−(Ca2+)2(2e−). The dimer [Ca(Ni@Ge9)]2(Ca)4 has not excess electron orbital expected and Ne = 0 (see Figure 2). Two Ca atoms appear as bridge connecting to two Ni@Ge9 units, so nonbridge 4 Ca atoms act as electron source and provide eight valence electrons to the chain skeleton, which shows that the dimer is a Ca salt and can described as [Ca2 (Ni@Ge9)2]8−(Ca2+)4. The trimer Ca[Ca4(Ni@Ge9)3](Ca)4 has two doubly occupied excess electron orbitals and four excess electrons, which are equivalent to the contribution from two Ca atoms. The nine Ca atoms minus the sum of the two Ca and four bridge Ca atoms equal to three Ca atoms which donate six electrons to the chain skeleton. Therefore, the trimer has a skeleton polyanion of −6. The trimer is a molecular all-metal electride chain and can be written as Ca2+[Ca4(Ni@Ge9)3]6−(Ca2+)4(4e−). The tetramer Ca2[Ca6(Ni@Ge9)4](Ca)4 has 12 Ca atoms including the two Ca (as four excess electrons source) and six bridge Ca atoms, and then four Ca atoms as electron source donate eight electrons to the chain skeleton. Then the tetramer is a
Table 2. Molecular Excess Electron Number (Ne), First Vertical Ionization Potential (VIP, in eV), HOMO−LUMO Gap (in eV), and Chain Scission Energy (Ecs1 and Ecs2, in kcal/mol) at the PBE0 Level monomer dimer trimer tetramer
Ne
VIP
gap
Ecs1
Ecs2
2 0 4 4
5.276 5.033 4.779 4.642
1.576 1.474 1.287 1.237
97 102 91
77
the precise evolution of electronic stabilities of these all-metal multicage chains is a monotone decreasing pattern for n = 1−4. For these all-metal multicage chains [(Ni@Ge9)Ca3]n (n = 1, 2,
Figure 3. Evolutions of VIP and H−L Gap with cage number are a monotone decreasing pattern. D
DOI: 10.1021/acs.jpcc.7b06464 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Table 3. Molecular Cage Number (n), Excess Electron Number (Ne), Transition Energy ΔE (eV), Oscillator Strength f 0, and Difference in the Dipole Moment between the Ground and the Crucial Excited State Δμ (D) from the TD-B3LYP Theory, Proportion of the Selected Excited States, Static Electronic First Hyperpolarizability βe0, Vibrational Harmonic First Hyperpolarizability βnr 0 (au). and βtl from the Two-Level Mode at the B3LYP Level monomer dimer trimer tetramer a
n
Ne
ΔE
f
Δμ
βtl
1 2 3 4
2 0 4 4
2.3405 1.3019 1.0549 1.1642
0.2141 0.0963 0.1090 0.0749
5.0093 0.0427 1.8834 6.2502
5968 133 12476 21165
transitiona 0.5 0.6 0.6 0.7
(H (H (H (H
− 6 → L + 1) − 2 → L) → L + 3) − 2 → L + 1)
βe0
βnr 0
e βnr 0 /β0
9321 27 21937 54232
1656 28 15330 63400
0.18 1.04 0.70 1.17
H = HOMO, L = LUMO.
3 and 4), the VIP values of 4.642−5.276 eV are slightly larger than the reported values of electride molecules: 4.16 for Li@ calix[4]pyrrole,16 4.20 for LiCNLi@BNNT,72 and 4.40 eV for CuAg@Ca8,25 but smaller than 5.56 for molecular all-metal electrides Mg(Ni@Pb12)Mg26 and the large value 7.78 eV of the electride molecule with the excess electron protected inside the C36F36 cage.73 This shows that these molecular all-metal multicage chains exhibit moderate electron stability. Considering their stabilities, antioxidation is still needed due to the existence of excess electrons. It is well-known that the HOMO−LUMO (the highest occupied molecular orbital and the lowest unoccupied molecular orbital) gap is a useful quantity for examining the molecular chemical stability. A large gap value reflects a high chemical stability. Table 2 lists the HOMO−LUMO (H−L) gaps of these [(Ni@Ge9)Ca3]n multicage chains (n = 1−4). The H−L gap evolution with increasing molecular chain length (or metal cage number n) has also a monotone decreasing pattern (see Figure 3). The gaps of the all-metal multicage chains are in the range of 1.237−1.576 eV, which are slightly smaller than those of organic electride.72,74−76 However, these H−L gap values are larger than those of 0.96−1.45 for molecular all-metal electrides M(Ni@Pb12)M (M = Be, Mg and Ca)26 and 1.03 or 0.99 for the all-metal clusters with interstitial La ion.77 Therefore, these studied all-metal multicage chains have the chemical stabilities close to those of some organic electrides and all-metal clusters. In order to exhibit chain scission stabilities of these all-metal polymer chains, calculated chain scission energy (Ecs) values for the dimer, trimer and tetramer are listed in Table 2. These Ecs values are 77−102 kca/mol involving two Ge−Ca bridge bond breakage, which is far larger than the depolymerization enthalpy of 17.7 ± 1.7 kJ for polymerized phase of C60,78 are comparable or larger than the bond energy of 80 kca/mol for C−C bond and less than that of 146 kca/mol for CC bond. This indicated that these all-metal multicage chains have strong enough stability. In the tetramer, Ecs1 = 91 for the chain scission in first bridge >Ecs2 = 77 kca/mol for the chain scission in the middle bridge shows the middle Ge−Ca bond is weaker (see Figure 1). 3.4. Static First Hyperpolarizabilities. 3.4.1. Static Electric and Vibrational First Hyperpolarizabilities. Now, we focus on the effects of the cage number and the excess electron number on the static first hyperpolarizability. The calculated static first hyperpolarizabilities for all-metal electride multicage chains are exhibited in Table 3 and Figure 4. The order of the βe0 values is 9321 for monomer >27 for dimer
